The Right Representation for Discovery: Finding the Conservation of Momentum

The representation of knowledge has a central role in the processes of discovery. A representation includes both the declarative formalisms that express knowledge and the procedural operators that are used to manipulate the formalisms. The role of representations in discovery is investigated by examining a case of law induction, the discovery of the conservation of momentum, using two different representations: (i) mathematical sentences and (ii) diagrams. The discovery is unlikely under the mathematical approach but feasible under the diagrammatic approach, as demonstrated by a computational model that simulates the discovery. Comparison of the approaches demonstrates again that the right representations are important for success in discovery and highlights the advantages in this instance of the diagrammatic representation, which include: the ability to encode information conveniently about the geometry of experimental setups; methods for comparing magnitudes of different properties; the possibility of organizing items of information deliberately to aid in making inferences; and, permitting the use of computationally inexpensive perceptual inferences.